Question

how many identical metal cones should be melted to form a cylinder that has twice the radius and twice the height of one of those cones?
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Answer 1

Given,

Height / radius of the cylinder = 2× Height / radius of one single cone.

To find,

Number of cones that we need to melt.

Solution,

Let, the height of the cone = h unit

And, let the radius of the cone = r unit

So,

Height of the cylinder = 2h unit

Radius of the cylinder = 2r unit

Now,

Volume of one cone = ⅓ πr²h unit³

Volume of the cylinder = π×(2r)²×2h = π×4r²×2h = 8πr²h unit³

Number of cones needed :

= Volume of cylinder/Volume of cone

= 8πr²h ÷ (πr²h/3)

= 8πr²h × 3/πr²h

= 8×3

= 24

Hence, we need to melt 24 cones.